Metabolic acidosis (MAc) is a common and potentially life-threatening acid–base disorder in mammals, including humans. It is caused by a depletion of extracellular (o) HCO₃ ⁻, which leads to a decrease in both [HCO₃ ⁻]_o and pH_o. In a living animal, MAc generally triggers a compensatory increase in ventilation, which lowers [CO₂]_o and thereby mitigates the decrease in pH_o. Under these conditions, all three fundamental CO₂/HCO₃ ⁻ acid–base parameters underwent changes, making it difficult to attribute the effects of compensated MAc to decreased [HCO₃ ⁻]_o, decreased pH_o, or decreased [CO₂]_o—or some combination of the three.

In vitro, we can equilibrate artificial solutions with a known partial pressure of CO₂, thereby preventing changes in [CO₂]_o. Even under these conditions, however, MAc is usually associated with two altered parameters—a decrease in [HCO₃ ⁻]_o and a decrease in pH_o—therefore, it is still difficult to know whether the effects of MAc are due to the reduction in [HCO₃ ⁻]_o per se or pH_o per se.

In addition to MAc, the three other fundamental acid–base disturbances (see Boron, 2017) are metabolic alkalosis (MAlk), in which an increase in [HCO₃ ⁻]_o causes pH_o to increase; respiratory acidosis (RAc), in which an increase in [CO₂]_o causes pH_o to decrease; and respiratory alkalosis (RAlk), in which a decrease in [CO₂]_o causes pH_o to increase. In all of these cases, the disturbance in an intact animal leads to changes in all three acid–base parameters, along the lines discussed in the first paragraph. In the laboratory, it is possible—under equilibrium conditions—to change two at a time.

A breakthrough occurred in 1995 with the development of a rapid-mixing approach for generating out-of-equilibrium (OOE) CO₂/HCO₃ ⁻ solutions (Zhao et al., 1995), which—over a wide range of pH values—can have any combination of [CO₂]_o, [HCO₃ ⁻]_o, and pH_o.

The use of OOE solutions offers a promising approacht o determining the extent to which individual acid–base parameters contribute to the physiological effects of MAc. The first such study was by Zhao et al. (2003), who found—on a background of a normal CO₂/HCO₃ ⁻ solution—that the isolated removal of basolateral (BL; i.e., blood-side) HCO₃ ⁻ from isolated, perfused proximal tubules (PTs)—leaving [CO₂]_BL and pH_BL unchanged—caused the rate of transepithelial HCO₃ ⁻ reabsorption (J _HCO3 ), measured over ∼20 min, to increase. Thus, this challenge—the most extreme possible example of MAc but without acidosis—produced the appropriate compensatory response.

Extending the work of Zhao and her coworkers, Zhou et al. (2005) used OOE solutions in a study in which they systematically varied [CO₂]_BL between 0% and 20% (leaving [HCO₃ ⁻]_BL and pH_BL fixed), varied [HCO⁻ ₃]_BL from 0 mM to 44 mM (leaving [CO₂]_BL and pH_BL fixed), or varied pH_BL from 6.8 to 8.0 (leaving [CO₂]_BL and [HCO⁻ ₃]_BL fixed). Surprisingly, they found that acute ¹ changes in pH_BL had no effect on J _HCO3 over the ∼20-min duration of the challenges. However, starting at conditions that mimicked the composition of normal arterial blood—[CO₂]_o = 5%, [HCO₃ ⁻]_o = 22 mM; pH_o = 7.40—isolated changes in [CO₂]_o or [HCO₃ ⁻]_o produced the appropriate compensatory effects:

(1) Isolated decrease in [HCO₃ ⁻]_o ([CO₂]_o and pH_o constant). Bouyer et al. (2024) named this disturbance “pure metabolic/down (pMet↓).” It is the metabolic part of MAc but without acidosis. Both Zhao et al. (2003) and Zhou et al. (2005) found that pMet↓ caused J _HCO3 to increase, which would tend to compensate for MAc.

In a somewhat different protocol, Bouyer et al. (2003) started with a rabbit PT exposed on both the apical (i.e., lumen) and basolateral sides to a CO₂/HCO₃ ⁻-free solution. Adding equilibrated CO₂/HCO₃ ⁻ to the basolateral side caused a rapid increase in [Ca²⁺]_i, whereas adding CO₂/HCO₃ ⁻ to the lumen had no effect on [Ca²⁺]_i. Switching to an OOE basolateral solution that contained physiological CO₂ but not HCO₃ ⁻ (“pure CO₂”) replicated the increase in [Ca²⁺]_i, whereas switching to an OOE basolateral solution that contained physiological HCO₃ ⁻ but not CO₂ (“pure HCO₃ ⁻”) had little effect on [Ca²⁺]_i. Thus, it may be that it is basolateral CO₂—in part acting through Ca²⁺—that triggers an increase in J _HCO3 in PTs. With our current knowledge of receptor protein tyrosine phosphatase γ (RPTPγ), we would now hypothesize that—if we started with equilibrated CO₂/HCO₃ ⁻ in the luminal and basolateral solutions—an isolated decrease in [HCO₃ ⁻]_o would have the same effect on [Ca²⁺]_i as would increasing [CO₂]_o.

The results of Zhao et al. (2003), Bouyer et al. (2003), and Zhou et al. (2005) were the first to unequivocally demonstrate that, independent of pH, each of the two components of the major blood buffer—CO₂ and HCO₃ ⁻—can act as acute, potent modulators of a biological function.

In an earlier study of cultured rat neurons, Bouyer and colleagues (2004) examined the effects of all four fundamental acid–base disturbances on the pH_i of both medullary-raphé (MR) neurons and HC neurons. For MAlk, RAc, and RAlk (but not MAc), both MR and HC neurons exhibited fully reversible pH_i changes, with ΔpH_i/ΔpH_o ratios of ∼60%. For MAc, the responses were more intriguing. Although most MR neurons and some HC neurons exhibited a ΔpH_i/ΔpH_o of ∼65%, some MR neurons and most HC neurons exhibited a ΔpH_i/ΔpH_o of only ∼9% (Bouyer et al., 2004). Later, Salameh and colleagues (2014) coined the terms “MAc-sensitive” and “MAc-resistant” to describe cells like those reported by Bouyer in response to a single acid–base challenge. Interestingly, and apropos of the most recent paper by Bouyer et al. (2024), Bouyer’s 2004 neurons that we would now term MAc-resistant, when switched from a MAc solution to a control solution, they often exhibited a pH_i rebound to a value above the initial baseline pH_i. A theoretical analysis led Bouyer et al. (2004) to hypothesize that the MAc-resistant neurons have a sensor for extracellular HCO₃ ⁻ and that a decrease in [HCO₃ ⁻]_o triggers an immediate stimulation of neuronal acid–base transporters that minimizes the MAc-induced decrease in pH_i.

Salameh et al. (2014), based on observed MAc-induced pH_i changes in 10 cell types, proposed that the demarcation between MAc-resistant and MAc-sensitive is a (ΔpH_i)/(ΔpH_o) of 40%. They pointed out that any such quantitative criterion is somewhat arbitrary.

Salameh et al. (2014) also extended the protocol of Bouyer et al. (2004) by including two successive MAc challenges, MAc₁ and MAc₂, separated by a period of recovery in a control CO₂/HCO₃ ⁻ solution. Comparing the pH_i induced by MAc₂ vs. MAc₁, they categorized neurons as “adapting” to the MAc challenge when ΔpH_i during MAc₂—(ΔpH_i)_2/MAc—was sufficiently smaller in magnitude than (ΔpH_i)_1/MAc, being “consistent” if the two ΔpH_i values were reasonably close and “decompensating” if the magnitude of (ΔpH_i)_2/MAc was sufficiently greater than that of (ΔpH_i)_1/MAc.

In their recent paper, Bouyer et al. (2024) expanded upon previous work by examining substitutions of pAc or pMet↓ for MAc in HC rat neurons in primary culture. They referred to resistance and sensitivity as two relative “states” of neurons, defined for single challenges (e.g., MAc₁ and MAc₂). They also referred to adaptation, consistency, and decompensation, defined for the transition from the first to the second challenge, as three “behaviors.”

In her PhD dissertation, Taki (2024) examined the twin challenges of MAc and RAc in murine co-cultures of HC neurons and astrocytes. Analyzing their data along the lines of Bouyer et al. (2024), Taki et al. found that the global knockout of RPTPζ, a candidate sensor of [CO₂]_o and [HCO₃ ⁻]_o expressed mainly in the central nervous system (CNS), led to much larger acidifications than those observed in cells from WT mice.

In the following sections ² , we provide a more formal presentation of state and behavior, along with methods for assessing them.

In the paper by Bouyer et al. (2024), the major contribution is the use of OOE solutions to dissect the contributions of the two components of MAc: the decreased pH_o per se and the decreased [HCO₃ ⁻]_o per se. The key to understanding OOE technology is the fact that the interconversion between CO₂ and H₂O, on one hand, and H⁺ and HCO₃ ⁻, on the other hand, involves two reactions, one of which is very slow and the other is very fast. The OOE approach separates chemical species on opposite sides of the slow reaction in the following sequence: CO 2 + H 2 O   ⇌ s l o w   H 2 CO 3   ⇌ f a s t   H + + HCO 3 − . (1)

Although we can independently control [CO₂]_o, [H⁺]_o (i.e., pH_o), and [HCO₃ ⁻]_o per se, we have less influence over other chemical species that depend directly or indirectly on any of the entities in the preceding two-step reaction. An important example is [CO₃ ⁼]_o, which depends on both [H⁺]_o and [HCO₃ ⁻]_o: HCO 3 −   ⇌   H + + CO 3 = . (2)

Moreover, the concentration of the NaCO₃ ⁻ ion pair depends on both [Na⁺]_o and [CO₃ ⁼]_o (as in Equation 3): Na + + CO 3 = ⇌   NaCO 3 −   , (3)

CO 3 = and NaCO₃ ⁻ are important for pH_i homeostasis because they are potential substrates of Na⁺-coupled HCO₃ ⁻ transporters as our group suggested in the 1980s and 1990s (Boron and Boulpaep, 1983; Boron and Russell, 1983; Boron, 1985; Boron and Knakal, 1989; 1992). A combination of electrophysiological and mathematical modeling approaches now shows that either Na⁺ + CO₃ ⁼ or NaCO₃ ⁻ is the actual substrate of both the electrogenic Na/HCO₃ cotransporter NBCe1 and the Na⁺-driven Cl-HCO₃ exchanger NDCBE (Lee et al., 2023). Because both transporters—and closely related members of the “solute-linked carrier” 4 (SLC4) family—play important roles in pH_i regulation of both neurons and astrocytes, it is instructive to consider how our experimental challenges impact [CO₃ ⁼]_o.

If we assume for a moment that the second reaction in Equation 1 is infinitely slow—and if the reaction sequence in Equation 1 represents the only significant pathway between CO₂/H₂O and H⁺/HCO₃ ⁻—then it is easy to observe how we could control [CO₂] independently of [H⁺] and [HCO₃ ⁻] and vice versa. The “slow” reaction in Equation 1 is slow enough that we can exploit it to make OOE solutions. The principle behind the OOE approach is to mix, with sufficient speed, two dissimilar CO₂/HCO₃ ⁻/pH solutions.

In addition to the reactions shown in Equation 1, which is typically the pathway shown in textbooks (see Boron, 2017), a parallel mechanism also converts CO₂ to HCO₃ ⁻: CO 2 ⏟ 0.0012 M + OH − ⏟ 3.16 × 10 − 7 M   → k 1 = 4 × 10 3   L ⋅ mol − 1 ⋅ s − 1 25   C o   HCO 3 −   . (4)

The concentration values below the braces approximately correspond to a physiological partial pressure of CO₂ (P_CO2 ) and a pH value of 7.5 at 25°C. Multiplying these concentration values by the forward rate constant yields a reaction velocity of v CO 2 + OH − = 4 × 10 3   L ⋅ mol − 1 ⋅ s − 1 × 1.2 × 10 − 3  mol ⋅ L − 1 × 3.16 × 10 − 7 mol ⋅ L − 1 ≅ 1.5 × 10 − 6 M ⋅ s − 1 = 1.5 × 10 − 3 mM ⋅ s − 1   . (5)

In the case of the first reaction in Equation 1, CO 2 ⏟ 0.0012 M + H 2 O   → k 1 = 0.036   s − 1 25   C o   H 2 CO 3 , (6) the forward rate constant predicts a reaction rate of v CO 2 + H 2 O = 3.6 × 10 − 2   s − 1 × 1.2 × 10 − 3  mol ⋅ L − 1 ≅ 4.3 × 10 − 5 M ⋅ s − 1 = 4.3 × 10 − 2 mM ⋅ s − 1   . (7)

H₂CO₃, the product of the “CO₂ + H₂O” reaction in Equation 6, would rapidly break down to form H⁺ and HCO₃ ⁻. Thus, it is reasonable to compare the velocity (Equation 7) of the “CO₂ + H₂O″ reaction in Equation 6 with that of the “CO₂ + OH⁻” reaction in Equation 4, which is only ∼3.5% as fast (Equation 5). This is why the OH⁻reaction in Equation 4 is generally ignored at physiological blood pH. However, the OH⁻pathway in Equation 4 is strikingly pH-sensitive because as pH increases, [OH⁻] increases exponentially. Thus, at a pH value of 9.0, the velocity of the “CO₂ + OH⁻” reaction in Equation 4 is already 11% greater than that of the “CO₂ + H₂O” reaction in Equation 6. At pH 10.0, it is 11-fold faster and so on.

The pH sensitivity of the OH⁻reaction has important implications for generating OOE solutions. Imagine that you wanted to generate a “pure CO₂ solution,” one with a physiological [CO₂] but almost no HCO₃ ⁻ at pH 7.4. You might be inclined to mix a CO₂ solution at low pH (e.g., 5.4, where most of the carbon would be in the form of CO₂) with a CO₂/HCO₃ ⁻-free solution at a very high pH (e.g., 10). However, you will find that your final [CO₂] will be much lower than expected, whereas your final [HCO₃ ⁻] will be much higher. The reason, it seems, is that the macroscopic mixing process described in Figure 1 initially generates microdomains that contain unmixed versions of the acidic/high-CO₂ solution and the very alkaline solution. At the interface, the reaction CO₂ + OH⁻ → HCO₃ ⁻ unexpectedly consumes your CO₂ and disrupts your anticipated near-HCO₃ ⁻-free state.

Another reaction can also wreak havoc with the creation of OOE solutions. Assume that you wanted to generate a “pure HCO₃ ⁻” solution, one with a physiological [HCO₃ ⁻] but almost no CO₂ at pH 7.4. You might be inclined to mix an HCO₃ ⁻ solution at a high pH value (e.g., 9.4, where most of the carbon would be in the form of HCO₃ ⁻ and CO₃ ⁼) with a CO₂/HCO₃ ⁻-free solution at a very low pH value (e.g., 5). However, you will find that your final [HCO₃ ⁻] will be much lower than expected, whereas your final [CO₂] will be much higher. The reason is that the hypothesized microdomains contain unmixed versions of the alkaline/high-HCO₃ ⁻ solution and the very acidic solution. At the interface, the reaction H⁺ + HCO₃ ⁻ → H₂CO₃ rapidly consumes HCO₃ ⁻ while increasing [H₂CO₃] to very high levels, whereupon the reaction H₂CO₃ → CO₂ + H₂O disrupts your anticipated near-CO₂-free state.

The challenges described in the preceding two paragraphs are discussed in conjunction with figure 1 in Zhao et al. (2003).

Figure 1A shows how to generate a “pure acidosis” (pAc) solution by rapidly mixing “solution 5a” and “solution 5b,” as defined in table ³ 1 in the paper by Bouyer et al. (2024). At the instant the two solutions combine, the “mixture” comprises (except for pH, which is complicated by buffer reactions) ½ A and ½ B. By trial and error (and making small pH adjustments to solution 5b, which contains the non-HCO₃ ⁻ buffer HEPES), one can achieve the desired pH_o (i.e., 7.20 in the case of pAc) and the desired [CO₂]_o of (10% + 0%)/2 = 5% and the target [HCO₃ ⁻]_o of (44 mM + 0 mM)/2 + 22 mM.

The abovementioned solution is out of equilibrium at the instant of mixing but gradually degrades to equilibrium as the solution approaches the experimental chamber over a period of ∼100 ms. The [CO₂]_o/[HCO₃ ⁻]_o ratio dictates a pH value of 7.4, although the actual pH_o value is 7.20 (i.e., higher [H⁺]_o). Because [H⁺]_o is too high for the extant [CO₂]_o/[HCO₃ ⁻]_o ratio, the chemical reaction as decribed in Equation 8 H + + HCO 3 − → f a s t H 2 CO 3 → s l o w CO 2 + H 2 O (8) proceeds (i.e., to consume excess H⁺ so that pH_o will slowly increase) until both the CO₂/HCO₃ ⁻ and HEPES buffer systems are simultaneously in equilibrium. We estimate that slight (∼1%) degradation occurs as the newly mixed solution approaches the chamber and that another 1% degradation may occur as the solution flows through the chamber for removal at the other end. Thus, this technology continuously generates the desired OOE solution “online”.

Figure 1B illustrates how to generate a “pure metabolic/down” (pMet↓) ⁴ solution by mixing “solution 6a” and “solution 6b,” as defined in table 1 in Bouyer et al. (2024). The approach is similar to that outlined above for pAc, except that our titration targets a pH_o value of 7.40 and a [HCO₃ ⁻]_o value of (28 mM + 0 mM)/2 + 14 mM. In this case, the [CO₂]_o/[HCO₃ ⁻]_o ratio of (5%)/(14 mM) dictates a pH value of 7.20, although the actual pH_o value is 7.40 (i.e., lower [H⁺]_o). Because [H⁺]_o is too low for the extant [CO₂]_o/[HCO₃ ⁻]_o ratio, the chemical reactions as decribed in Equation 9 CO 2 + H 2 O   → s l o w   H 2 CO 3   → f a s t H + + HCO 3 − (9) proceed (i.e., to generate H⁺ so that pH_o will slowly decrease) until both the CO₂/HCO₃ ⁻ and HEPES buffer systems are simultaneously in equilibrium.

Zhao and colleagues (2003) examined many of the technical details of employing OOE solutions, particularly in isolated, perfused renal PTs.

“State” describes the degree of pH_i change—resistant vs. sensitive—as it applies to each challenge. The state is not a quantum value—like the distinct “on” and “off” positions of a light switch—but rather like the relative brightness of a light controlled by a dimmer mechanism. The distribution of pH_i changes in response to MAc is more or less continuous, and the designation as resistant or sensitive is a semi-quantitative description.

In Figure 2A, we reproduce—for the reader’s convenience—three pH_i recordings from Bouyer et al. (2024). The blue record represents one of the neurons in the MAc–MAc protocol of figure 3a of Bouyer et al. (2024). The red record is from the pAc. MAc protocol of figure 6a. The green record is from the MAc-pMet↓ protocol of figure 9a.

In Figure 2B, the single axis (i.e., x-axis) represents the (ΔpH_i)₁ for each of the three neurons in panel A. Following the “40%” definition of Salameh et al. (2014), the vertical dashed blue line represents the demarcation between “resistant” and “sensitive” neurons for (ΔpH_i)₁. Because ΔpH_o was 0.2, this blue line is 40% × 0.2 = 0.08 pH units to the left of where the y-axis would be (represented by the vertical gray line). The 40% figure emanates from a study of multiple cell lines and represents a natural break in the data (see Salameh et al., 2014). Because this figure is somewhat arbitrary, one could imagine adjusting it to match the degree of MAc or the nature of a disturbance (e.g., MAc vs. MAlk vs. RAc). We have chosen to adhere to the original definition to facilitate data comparisons.

• The red point representing (ΔpH_i)_1/pAc lies just to the left of the vertical dashed blue line because pAc₁ resulted in a pH_i decrease of 0.084 (i.e., the point is 0.084 to the left of the vertical gray line).

All three neurons are in the green (ΔpH_i)₁ sensitive zone.

In Figure 2C, the single axis (i.e., y-axis) represents (ΔpH_i)₂ for each of the same three neurons in panel A. The horizontal dashed blue line represents the demarcation between “resistant” and “sensitive” neurons for (ΔpH_i)₂ and is 0.08 pH units below where the x-axis would be (represented by the horizontal gray line).

• The red point representing (ΔpH_i)_2/MAc lies well below the horizontal dashed blue line because MAc₂ resulted in a pH_i decrease of 0.208 (the point is 0.208 below the horizontal gray line).

The blue and red neurons are both in the green (ΔpH_i)₂ sensitive zone, whereas the green neuron is in the peach-colored (ΔpH_i)₂ resistant zone (which also includes paradoxical alkalinizations).

Figure 2D shows an overlay of panels B and C. The intersecting blue dashed lines now define four quadrants (Q):

• I. Any neurons in Q_I are resistant for both (ΔpH_i)₁ and (ΔpH_i)₂.

“Behavior” describes the change in ΔpH_i in the transition from the first to the second challenge. By definition, behavior has meaning only for two or more challenges. We term the graphical representation of behavior the “hourglass plot” (Figure 2E), which we build around the line of identity (LoI) that describes an experimental result, in which (ΔpH_i)₂ = (ΔpH_i)₁. This is the dashed gray line running from the lower left, through the origin, to the upper right. The curved parts of the hourglass represent confidence limits, as defined by Salameh et al. (2014) and described mathematically in equations 1 and 2 of the paper by Bouyer et al. (2024). Although the precise values of confidence limits are somewhat arbitrary, the hourglass provides an indication of the following behaviors:

• A “consistent” behavior is one in which the point representing the neuron lies within the hourglass, as typified by the blue neuron, which lies on the LoI.

Note that—as defined by Salameh et al. (2014)—a change in state does not necessarily produce an adaptive or decompensating behavior (the change in ΔpH_i must be sufficiently large). Conversely, the behavior can be adaptive or decompensating, although the state does not change (e.g., a point can be above or below the hourglass in Q_I).

The hourglass analysis provides a useful visual display. However, from a quantitative perspective, it categorizes a cell only in a ternary fashion (i.e., adaptive, consistent, and decompensating) and can categorize a population only by referring to fractions of cells with particular behaviors. Bouyer et al. (2024) introduced two variations in these concepts, in which one computes the distance of a point to the LoI. Figure 2F shows five points. Blue, red, and green represent the three neurons from panel A; the pink and gold points are two arbitrary examples from figure 3b of the recent Bouyer paper. The dashed line associated with each point represents the distance from the point to the LoI.

In one variation, the distance is unsigned (d _Absolute)—all values are positive distances—so that average d _Absolute describes the dispersion of the points from the LoI.

In the other variation, the distance is signed d _±. Positive d _± values (e.g., gold and green points)—represent points above/to the left of the LoI and thus describe the strength of adaptation. Negative values (e.g., pink and red points) represent points below/to the right of the LoI and thus describe the strength of decompensation. The blue point lies virtually on the LoI and thus has a d _± value of ∼0. The mean d _± value of a population describes the overall direction and “behavior strength”—a term coined in the dissertation by Taki (2024). An advantage of the d _± approach is that one can perform statistical tests on populations of cells (e.g., wild-type vs. knockout).

Figure 3A illustrates the major acid-extrusion and acid-loading mechanisms in a cell such as a CNS neuron. Two reviews consider the detailed properties of these transporters, including sensitivity to acid–base challenges (Ruffin et al., 2025; Thornell et al., 2025).

As described previously (Roos and Boron, 1981; Boron, 2004; Bevensee and Boron, 2013; Occhipinti et al., 2020; Thornell et al., 2025), the fundamental law of pH_i regulation is d pH i d t = ρ β ⋅ J E − J L . (10)

Here, dpH_i/dt is the time rate of change of pH_i; ρ is the surface-to-volume ratio of the cell; β is total intracellular buffering power; J _E is the sum of the rates of all individual acid-extrusion processes (the rates of which are J _E1, J _E2, etc.), such as those on the left side of Figure 3A; and J _L is the sum of the rates of all individual acid-loading processes (the rates of which are J _L1, J _L2, etc.), such as those on the right side of Figure 3A.

As illustrated in Figure 3B, J _E tends to increase as pH_i decreases, whereas J _L tends to have the opposite pH_i dependence. In a steady state (i.e., when dpH_i/dt = 0), pH_i is stable because J _E = J _L. An acid–base challenge can initiate a change in pH_i (i.e., displace dpH_i/dt from 0) only by altering J _E and/or J _L, which, in turn, can occur only by producing near-instantaneous effects on transporters (factor ‘1,’ above) or sensors that rapidly regulate transporters (factor ‘2’). The subsequent time course of pH_i depends on evolving changes in J _E and J _L, which, in turn, must reflect changes in cellular properties—for example, ΔpH_i, Δ[HCO₃ ⁻]_i, Δ[CO₃ ⁼], and other downstream parameters—that secondarily modulate the pH_i dependence and other kinetic properties of transporters. Thus, the evolving pH_i dependencies of J _E and J _L determine the new steady-state pH_i, at which J _E and J _L come into balance during the challenge. These evolving changes could not only affect what we observe as the “state” during challenge #1, but they could also be sufficiently long-lasting to affect the “state” during challenge #2, thereby revealing themselves as “behavior.”

Note that changes in ρ or β cannot affect steady-state pH_i and, thus, cannot underlie a resistant/sensitive phenotype (i.e., state) or an adaptive/consistent/decompensative phenotype (i.e., behavior). ⁵

In the following analyses, the effects of acid–base challenges on transporters would be rapid-onset/rapid-offset but, as noted in the previous section, could evolve during the challenge.

The introduction of the paper by Bouyer et al. (2025), the review by Ruffin et al. (2025), and the work by Thornell et al. (2025) summarize several classes of acid–base sensors. GPR68 (OGR1) is one of at least four pH_o-sensitive G-protein-coupled receptors (GPCRs) and is present in medulloblastoma tissue (Huang et al., 2008), rat HC neurons (Schneider et al., 2012), and rat anterior pituitary gland (Horiguchi et al., 2014). Figure 6 depicts GPR68, in particular, and the presumed effects of MAc. HC acid-sensing ion channels (ASICs) (Alvarez et al., 2003) could play a role as pH_o-sensors. On the other hand, although the tandem pore domain acid-sensing K⁺ (TASK) channels are present in multiple brain regions (Lesage, 2003), they are not in the hippocampus. Finally, the putative extracellular CO₂/HCO₃ ⁻ sensors, RPTPγ and RPTPζ, are widely distributed in the CNS (Müller et al., 2004; Hayashi et al., 2005; Lamprianou et al., 2006) and could potentially contribute to the pH_i physiology in the study by Bouyer et al. (2024). Recent work by Taki et al. (2024) shows that murine HC neurons (but not astrocytes) express both RPTPγ and RPTPζ. Moreover, in her PhD dissertation, Taki (2024) showed that the global knockout of RPTPζ in mice greatly reduces the ability of HC neurons to resist the pH_i decrease caused by MAc or RAc.

The activation of extracellular acid–base sensors, with a slight delay, could modulate the activity of acid–base transporters and thereby contribute to—or oppose—the initiation of pH_i changes predicted in Figure 5 during an acid–base challenge. The continuing actions of these extracellular sensors—that is, their effects on transporters and cellular constitution—likely impact the evolution of the pH_i change later during the challenge and produce longer lasting effects that influence “behavior” in the second of two challenges.

The effects of acid–base disturbances on transporters (see factor ‘1,’ just above) and extracellular sensors (see factor ‘2,’ above) could begin instantaneously or nearly so and continue throughout the challenge (Figure 7). Although, upon the removal of the challenge, the effects on transporters and sensors per se may cease just as instantaneously as they had commenced, the more slowly developing consequences of altered transporter activity on intracellular solute concentrations (e.g., pH_i, [HCO₃ ⁻]_i, [CO₃ ⁼]_i, [Na⁺]_i, and [Cl⁻]_i), membrane potential (V _m), and of altered sensor activation on downstream signaling pathways (e.g., phosphorylation state and protein trafficking) could evolve during the acid–base challenge and also persist for some time. ⁸ In addition to constitutional changes produced directly by acid–base transporters (‘1’) and extracellular sensors (‘2’), indirect influences could include myriad effects. For example, V _m changes could affect voltage-sensitive channels and transporters and thereby affect neuronal firing and such parameters as [Ca²⁺]_i. Alterations in ion concentrations would impact transporters and channels other than those depicted in Figure 3. For example, increased [Na⁺]_i would stimulate the Na–K pump, which would tend to lower [Na⁺]_i, increase [K⁺]_i, and hyperpolarize the cell. Changes in pH_i could directly impact pH_i sensors (reviewed by Thornell et al., 2025) and—because [HCO₃ ⁻]_i changes in the same direction as pH_i—could secondarily impact the soluble adenylyl cyclase sAC (Chen et al., 2000), present in some HC axon terminals (Chen et al., 2013). In locus coeruleus chemosensitive neurons, the activation of sAC increases L-type Ca²⁺-currents and limits the hypercapnia-induced increase in the firing rate (Imber et al., 2014).

The above mentioned effects could produce changes in the number of acid–base transporter proteins in the plasma membrane (due to trafficking, protein degradation, and eventually protein synthesis) and changes in their unitary or “per-molecule” activities (due to alterations in intracellular ionic and post-translational modifications). Thus, the “functional activity” of transporters (i.e., protein number × unitary activity) underlying many J _E1, J _E2, … and J _L1, J _L2, … terms introduced in our introduction of Equation 10 may change over the evolution of the acid–base disturbance and then persist for some time.

Taki (2024) suggests that in a MAc–MAc protocol, progressively lower and lower pre-MAc₂ pH_i values correlate with an increase in the degree of adaptation behavior. Because higher pH_i values just before MAc₂ translate to higher [HCO⁻ ₃]_i values just before MAc₂ (assuming that CO₂ has equilibrated across the cell membrane), it is possible that sAC (which senses cytoplasmic HCO₃ ⁻) could participate in neuronal state and/or behavior. Other pH_i-sensitive processes could respond during a challenge, and the extracellular sensors could affect these or vice versa.

In acutely dissociated HC CA1 neurons, Brett et al. (2002) have shown that the inhibition of protein kinase A (PKA) inhibits Cl-HCO₃ exchange but stimulates Na⁺-dependent Cl-HCO₃ exchange, thereby increasing pH_i in low-pH_i neurons. In high-pH_i neurons, the effects are the opposite. The stimulation of PKA has the opposite set of effects. In the protocols of Bouyer et al. (2024), decreases in pH_o could have activated pH_o ⁻ sensitive GPCRs that elevate [cAMP]_i (Radu et al., 2005) and thereby contributed to state and behavior.

Salameh et al. (2014) defined MAc-resistant cells as those for which pH_i decreases by <40% of ΔpH_o. Regardless of where one draws the dashed blue lines in Figures 2B, D, some cells will be more resistant/sensitive than others. Bouyer et al. (2024) observed a continuum of ΔpH_i values that presumably depend on the factors noted in the previous section: ⁹ rapid effects on ‘1’ acid–base transporters, ‘2’ extracellular acid–base sensors, and ‘3’ more slowly developing effects on cellular constitution. Figure 8A summarizes the interdependence of factors ‘1’–‘3’ for a naïve cell with an “average ¹⁰ ” pH_i decrease during MAc₁. The initial (i) steady-state pH_i (i.e., pH_i prevailing just before MAc) is described by the intersections of the semi-transparent blue and red curves. We now discuss the impact of MAc₁ on cells in four different states—sensitive and resistant plus “average” and “paradoxical” (an extreme variant of resistant)—and then raise the issue of how pAc₁ and pMet↓₁ contribute to MAc₁.

The three types of behavior must reflect persistent effects (or lack thereof) on the three factors introduced above ¹³ to produce, during MAc₂, a state that is the same, more resistant, or more sensitive than during the preceding MAc₁.

In the next three subsections, we (1) present hypotheses of how behaviors arise, (2) explore insights from the non-additivity of pAc₂ and pMet↓₂ [a conclusion reached in equations 6 & 7 of Bouyer et al. (2024)], and (3) consider parameters that could affect behavior.

Figure 12 presents cellular models of adaptation, consistency, and decompensation. In each case, the intracellular bright green “plus” boxes indicate stimulation of acid extrusion via some combination of the three factors: an increase in the number of transporters at the cell surface, an increase in the functional activity of extracellular sensors to increase J _E, and changes in the cellular constitution that increase the unitary activity of acid extruders. The red “minus” boxes indicate the opposite for acid loading. Note that, in our cellular models, increases in J _E and decreases in J _L are interchangeable because they could produce similar changes in Δ(J _E–J _L). For simplicity, we show equal numbers of “plus” and “minus” boxes. In Figure 12, panels A₁, A₂, and A₃ are identical.

In our presentation of Figure 11, we observed that, in a population of naïve neurons, the sum of ΔpH_i values in pAc₁ and pMet↓₁ is approximately equal to MAc₁. Figure 13 illustrates an analogous analysis of pAc and pMet↓ but for neurons previously challenged in period #1 with MAc.

Not addressed in the studies of Salameh et al. (2014) and Bouyer et al. (2024) are several important unresolved questions regarding the duration of events required for establishing behaviors:

We suggest that a fruitful initial approach for addressing the abovementioned questions could be to use the MAc-pMet↓ protocol as a test case because it produces the most reproducible and remarkable responses. Recall that figure 9b in the study of Bouyer et al. (2024) shows that ∼87% of neurons subjected to this protocol exhibit a paradoxical pH_i increase.

It is of interest that, in the study of Bouyer et al. (2024) and the PhD dissertation of Taki (2024), the initial MAc₁-induced pH_i decrease (indicative of a negatively shifted [J _E–J _L]) was not followed by a delayed pH_i increase (reminiscent of adaptation) or pH_i decrease (reminiscent of decompensation) during MAc₁. Thus, we can conclude that either (1) the duration of challenge #1 (e.g., 7 min in the Taki study) was too brief for the development of a secondary change in (J _E–J _L) or (2) the removal of challenge #1 is necessary for the development of the behavior observed during challenge #2.

Although we have primarily focused on acid–base parameters as potential modulators of behavior, other environmental factors—metabotropic signaling molecules and the ionic milieu (e.g., [K⁺]_o)—also could also be in play.

Both a relatively resistant state and an adaptive behavior could be the appropriate “selfish” response of neurons, for which a relatively large acidic pH_i shift would have a negative impact on the physiological role of analogous neurons in an intact brain. Such hypothetical neurons—those especially critical under a particular set of circumstances—may be programmed to reduce the magnitude of acidic shifts using the strategies outlined above. The price to pay for such selfishness is that the cell’s small negative (J _E–J _L) necessarily results in the extrusion of acid into the extracellular space (see Figure 9C and Figure 12B), which lays an extra low-pH_o burden on neighboring cells.

Both an average ¹⁰ state and a consistent behavior could be the appropriate “unselfish” response of neurons, for which an acidic pH_i shift would have a limited impact on the physiological role of an analogous neuron in an intact brain. By allowing themselves to acidify moderately during MAc₁ and/or to acidify no more during MAc₂ than during MAc₁, such neurons perform an important function by buffering extracellular acid and reducing extracellular acid loads experienced by neighboring cells.

Both a relatively sensitive state and a decompensating behavior could be the appropriate “altruistic” response of neurons, for which a relatively severe acidic pH_i shift would have limited impact on the physiological role of an analogous neuron in an intact brain. By allowing themselves to acidify to a relatively large degree during MAc₁, and/or acidifying more during MAc₂ than during MAc₁, these altruistic neurons buffer disproportionately greater fractions of extracellular acid loads and thereby spare their neighboring cells.

Although we have focused on neurons, it is interesting to recall that Salameh et al. (2014) found that, during a MAc–MAc protocol, ΔpH_i/ΔpH_o is consistently greater (by nearly 50%) for astrocytes than for neurons, both in cultures from the hippocampus and medullary raphé and both for MAc₁ and MAc₂. On the other hand, intrinsic intracellular buffering power (β_I; see Thornell et al. (2025) has the opposite pattern for the two cell types. For cultured astrocytes from rat HC, β_I is only ∼10 mM/pH at pH_i 7.0 in one study (Bevensee et al., 1997), whereas β_I of neurons acutely isolated from rat HC is much higher, ∼15 mM/pH at pH_i 7.0 in another study (Bevensee et al., 1996). Thus, if we consider only β_I, although their ΔpH_i may be 50% greater, HC astrocytes would take up about the same amount of acid per unit volume of cytosol as neurons. On the other hand, total intracellular buffering power (β_T) is the sum of β_I and the open-system CO₂/HCO₃ ⁻ buffering power (β_open), with the latter increasing exponentially ¹⁵ with pH_i and being the same in all cells. Thus, at relatively low pH_i values, β_T would be modestly lower in astrocytes than in neurons, and astrocytes (with a 50% greater ΔpH_i) would buffer modestly more acid than neurons. At relatively high pH_i values, β_open would overwhelm β_I, and thus, β_T would be rather similar in the two cell types; in this case, astrocytes would buffer much more acid than neurons. Because astrocytes can undergo rather large pH_i changes and buffer more acid than neurons on average, we could view them as being altruistic compared to neurons.

Changes in pH_o or pH_i can affect a wide range of electrophysiological properties because of the pH_i/pH_o sensitivity of virtually every neuronal component—including channels, receptors, transporters, enzymes (including those involved in neurotransmitter metabolism), and cytoskeletal elements. Thus, one would expect that inappropriate pH_i changes could lead to CNS pathology. It is generally believed that high neuronal pH_i is pro-epileptogenic (Hentschke et al., 2006; Jacobs et al., 2008; Sinning et al., 2011). Chesler and Kraig (1987), Chesler and Kraig (1989) and Ransom (2000) proposed a negative-feedback model, which was discussed and extended by Salameh et al. (2017). In this model, neuronal activity leads to an increase in [K⁺]_o, causing depolarization-induced alkalinization (DIA) in astrocytes (Siebens and Boron, 1989a; Siebens and Boron, 1989b), that in turn would cause a fall in pH_o—a local MAc—and, thus, a generalized reduction in neuronal excitability. We would expect that local MAc would lower neuronal pH_i. Induced epileptiform activity lowers neuronal pH_i, which recovers after the epileptiform activity ceases (Xiong et al., 2000; Raimondo et al., 2012). Although high pH_o is also considered to be pro-epileptogenic, chronic low-grade metabolic acidosis may contribute to the development of chronic epilepsy (Yuen, 2006).

Based on the above discussion, one might have expected the distribution of neuronal pH_i values to be within a relatively narrow range. However, a striking characteristic of mammalian HC neurons, freshly dissociated or cultured, is an unusually wide range of resting pH_i values (Schwiening and Boron, 1994; Baxter and Church, 1996; Bevensee et al., 1996; Smith et al., 1998) compared to other cell types. Moreover, our laboratory has identified a wide range of ΔpH_i responses to MAc (Bouyer et al., 2004; Salameh et al., 2014; 2017) and twin MAc–MAc challenges (Salameh et al., 2014; 2017). Bouyer et al. (2024) study confirms this diversity of responses to MAc (state) and MAc–MAc (behavior) and extends both aspects of diversity to the artificial acid–base disturbances pAc and pMet↓, alone and in combination with MAc.

We have already presented hypotheses to address the molecular mechanisms underlying the diversity of state and behavior. We now ask, at a higher level, what is responsible for the aforementioned diversity? We offer four possibilities that are not mutually exclusive.

(1) Some of the diversity is unphysiological. For example, the above-cited studies show that the broad range of initial pH_i values is greater in the absence than in the presence of CO₂/HCO₃ ⁻ (which would presumably enable the full complement of pH_i-regulatory mechanisms). It is possible that the range would be narrower still if we were to study the neurons in vivo, where they would be under the potential influence of metabotropic signaling and other influences from neighboring cells in a three-dimensional arrangement.

Thus, each neuron in culture could have a set of properties that depends on neuronal subtype, stochastic variations in protein numbers/localization within that subtype (nature), and differences in neuronal history (nurture). Together, these factors could establish a constitution that determines how a particular neuron responds to one acid–base challenge (state) or a sequence of them (behavior).

A teleological question that arises is why should such diversity exist? One advantage of diversity could be to increase the probability that enough neurons in a circuit can withstand periodic acid–base challenges of various types. Another could be that neurons with different electrophysiological properties (and the underlying cohort of ion channels and other proteins, each with its own pH_i sensitivity) could be more electrically stable with a resistant vs. sensitive state or with an adaptive vs. consistent vs. decompensatory behavior.

Regarding the experiments with OOE solutions, we believe that the main conclusions of the paper by Bouyer et al. (2024) can be summarized as follows.

Mouse HC neurons express both RPTPγ and RPTPζ (Lorenzetto et al., 2014; Taki et al., 2024). Based on the PhD dissertation of Taki (2024), who examined the effect of knocking out RPTPζ in MAc–MAc and RAc–RAc protocols on mouse HC neurons, and the work of Zhou et al. (2016), who examined the effect of knocking out RPTPγ in renal proximal tubules, we propose that the most likely HCO₃ ⁻ sensor(s) in the experiments of Bouyer et al. (2024) are some combination of RPTPγ and RPTPζ.

In addition, we urge additional experiments that further probe the molecular mechanisms underlying state and behavior and suggest an extension of the studies to include (1) the duration and intensity of the first challenge, (2) the duration of the recovery period, and (3) additional acid–base challenges that involve both equilibrated solutions (i.e., RAc, MAlk, and RAlk) and OOE solutions (pAlk, pMet↑, pResp↓, and pResp↑).

Aside from a call for more wet-laboratory data, we urge the development of mathematical models—the counterparts of the qualitative models described with words and cartoons in the present paper—that could assist in the interpretation of experiments like those in the research paper by Bouyer et al. (2024). Boron and De Weer (1976) developed the first mathematical model of pH_i regulation, a compartmental model that embodies the principles of the fundamental law of pH_i regulation in Equation 10. Occhipinti et al. (2020), as part of the Physiome journal (which is part of the broader Physiome Project), wrote a retrospective of the BDW model that includes clarifications and updates, access to online implementations, and a summary of several post-BDW models of pH_i regulation.

The set of two ordinary differential equations in the BDW model includes only one component of J _L (an H⁺ pump, the rate of which varies with [H⁺]_i—and thus time—according to a fixed rate constant) and a single component of J _E (an HCO₃ ⁻ leak, the rate of which varies with [HCO₃ ⁻]_i—and thus pH_i and time—according to a fixed HCO₃ ⁻ permeability). Although it would be straightforward to incorporate additional components of J _E (i.e., J _E1, J _E2, … ) and J _L (i.e., J _L1, J _L2, … ), imbuing these components (e.g., variants of NBCn1) with realistic estimates of sensitivity to pH_i and pH_o, as well as their respective substrates, would require major—but valuable—investments from funding agencies. The same applies to acid–base sensors and the broader issue of “cellular constitution,” which would describe diverse influences ranging from ion concentrations to signal transduction pathways.

Figure 14 is a cartoon model of how interactions among (1) transporters, (2) sensors, and (3) cellular constitution could account for the results of the recent study by Bouyer et al. (2024). As noted in the figure legend, the cartoon is greatly oversimplified: each transporter icon represents a multitude of individual proteins. The ↓pH_o and ↓[HCO₃ ⁻]_o sensors could represent multiple examples of each (see Figure 6). We defined constitution as “the collection of all ion-concentration, metabolic, and signaling properties.” All of the interconnected components vary with time during—and after—and acid–base challenge. Their dependencies on concentrations of their relevant substrates/ligands are almost certainly nonlinear. Effects could have varying degrees of additivity or antagonism.

A goal of programs such as The Physiome is to develop modular mathematical components for each transporter and signaling pathway, assemble the components into various model cells, and inform the models from experiments like those reported in the research paper by Bouyer et al. (2024). We envision the development of such sophisticated models—the quantitative versions of those qualitative models in the present paper—and using them to interpret the research paper by Bouyer et al. (2024) and design future experiments.

We begin by acknowledging the principle that “all models are wrong, but some are useful”—the first part of which is articulated by the British statistician Box (1976), who also emphasized the concept of “useful.”

The word and cartoon models presented in this paper are based on the fundamental law of pH_i regulation (see Equation 10), which is mathematically expressed as follows: d pH i dt = ρ β ⋅ J E − J L   . (11)

This equation is analogous to the principle of continuity in physiology ¹⁶ or fluid mechanics, which, in turn, is based on the conservation of mass. Thus, the basic model must be correct, at least at the integrative level of classical physics and chemistry.

The theoretical cartoon models presented in this paper could be tested by employing more sophisticated mathematical modeling approaches than that explained in Equation 10. These approaches could resort to “compartmental” models, treating the cell and the extracellular fluid as uniform compartments with instantaneous mixing (i.e., ignoring a detailed spatial description of the cell geometry and its effects on solute diffusion). More complex approaches could resort to 3D (“distributed”) reaction-diffusion models, in which one accounts for the diffusion (or transport) of solutes in 3D space/time, as well as the chemical reactions that occur in parallel 3D space/time. For example, such models can attempt to account for unconvected layers that surround a cell and how geometry impacts the time courses of solute concentrations. In either case, the modeler formulates the problem using differential equations and solves these using various numerical methods. Assumptions—and opportunities for error—abound at each conceptual step.

Limitations also arise in the complexity of the biological system and the oversimplifications by which we estimate individual terms, even in the relatively simplest of approaches (e.g., a compartmental system):